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A volume comparison theorem
for Finsler manifolds


Author: Carlos E. Durán
Journal: Proc. Amer. Math. Soc. 126 (1998), 3079-3082
MSC (1991): Primary 53C60, 53C15
DOI: https://doi.org/10.1090/S0002-9939-98-04629-2
MathSciNet review: 1473664
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $(M^{n},F)$ be a symmetric Finsler manifold, endowed with the Busemann volume form, and let $D$ be its unit disk bundle endowed with the canonical symplectic volume form. It is shown that $Vol(D)\leq C(n)Vol(M^{n})$, where $C(n)$ is the volume of the unit disk in ${\mathbb{R}}^{n}$. Moreover, equality holds if and only if $(M^{n},F)$ is Riemannian.


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Additional Information

Carlos E. Durán
Affiliation: IMPA, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janerio RJ 22460-320, Brasil
Address at time of publication: IVIC-Matematicas, Apartado 21827, Caracas 1020-A, Venezuela
Email: cduran@impa.br, cduran@cauchy.ivic.ve

DOI: https://doi.org/10.1090/S0002-9939-98-04629-2
Keywords: Riemannian geometry, Finsler geometry
Received by editor(s): March 6, 1997
Additional Notes: Supported by CNPq, Brasil
Communicated by: Christopher B. Croke
Article copyright: © Copyright 1998 American Mathematical Society